A Carnot engine operating between temperatures $${{T_1}}$$ and $${{T_2}}$$ has efficiency $${1 \over 6}$$. When $${T_2}$$ is lowered by $$62$$ $$K$$ its efficiency increases to $${1 \over 3}$$. Then $${T_1}$$ and $${T_2}$$ are, respectively:

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $$V$$ to $$32$$ $$V$$, the efficiency of the engine is

Two moles of helium gas are taken over the cycle $$ABCD,$$ as shown in the $$P$$-$$T$$ diagram.

Assuming the gas to be ideal the work done on the gas in taking it from $$A$$ to $$B$$ is :

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $$\theta $$ along the length $$x$$ of the bar from its hot end is best described by which of the following figures?